메뉴 건너뛰기




Volumn 178, Issue 1-2 SPEC. ISS., 2005, Pages 377-391

On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series

Author keywords

Elliptic hypergeometric series; Karlsson Minton type hypergeometric series; Matrix inversion

Indexed keywords

INVERSE PROBLEMS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS;

EID: 14844343264     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.02.028     Document Type: Article
Times cited : (23)

References (33)
  • 1
    • 1042287960 scopus 로고    scopus 로고
    • Bailey's transform, lemma, chains and tree
    • J. Bustoz M.E.H. Ismail S.K. (Eds.) Kluwer Academic Publisher Dordrecht
    • G.E. Andrews Bailey's transform, lemma, chains and tree, in: J. Bustoz M.E.H. Ismail S.K. (Eds.), Suslov Special Functions 2000: Current Perspectives and Future Directions 2001 Kluwer Academic Publisher Dordrecht 1-22
    • (2001) Special Functions 2000: Current Perspectives and Future Directions , pp. 1-22
    • Andrews, G.E.1
  • 2
    • 0031572792 scopus 로고    scopus 로고
    • Generalized bibasic hypergeometric series and their U(n) extensions
    • G. Bhatnagar S.C. Milne Generalized bibasic hypergeometric series and their U ( n ) extensions Adv. Math. 131 1997 188-252
    • (1997) Adv. Math. , vol.131 , pp. 188-252
    • Bhatnagar, G.1    Milne, S.C.2
  • 3
    • 0041978294 scopus 로고
    • Some multifold reciprocal transformations with applications to series expansions
    • W. Chu Some multifold reciprocal transformations with applications to series expansions Eur. J. Combin. 12 1991 1-8
    • (1991) Eur. J. Combin. , vol.12 , pp. 1-8
    • Chu, W.1
  • 4
    • 21344485564 scopus 로고
    • Partial-fraction and bilateral summations
    • W. Chu Partial-fraction and bilateral summations, J. Math. Phys. 35 (1994) 2036-2042
    • (1994) J. Math. Phys. , vol.35 , pp. 2036-2042
    • Chu, W.1
  • 5
    • 33845893808 scopus 로고
    • Erratum
    • W. Chu, erratum: J. Math. Phys. 36 (1995) 5198-5199
    • (1995) J. Math. Phys. , vol.36 , pp. 5198-5199
    • Chu, W.1
  • 6
    • 0012959027 scopus 로고    scopus 로고
    • Partial-fraction expansions and well-poised bilateral series
    • (Szeged)
    • W. Chu, Partial-fraction expansions and well-poised bilateral series, Acta Sci. Math. (Szeged) 64 (1998) 495-513.
    • (1998) Acta Sci. Math. , vol.64 , pp. 495-513
    • Chu, W.1
  • 7
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
    • V.I. Arnold et al. (Eds.) Birkhäuser Boston
    • I.B. Frenkel V.G. Turaev Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions, in: V.I. Arnold et al. (Eds.), The Arnold-Gelfand Mathematical Seminars 1997 Birkhäuser Boston 171-204
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.B.1    Turaev, V.G.2
  • 8
    • 0000267209 scopus 로고
    • Summation formulas for basic hypergeometric series
    • G. Gasper Summation formulas for basic hypergeometric series SIAM J. Math. Anal. 12 1981 196-200
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 196-200
    • Gasper, G.1
  • 9
    • 0037736197 scopus 로고    scopus 로고
    • Elementary derivations of summation and transformation formulas for q-series
    • M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.) Fields Institute. Communication 14, Providence RI
    • G. Gasper, Elementary derivations of summation and transformation formulas for q-series, in: M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.), Special Functions, q-Series and Related Topics, Fields Institute. Communication 14, Providence, RI, 1997, pp. 55-70.
    • (1997) Special Functions, Q-Series and Related Topics , pp. 55-70
    • Gasper, G.1
  • 11
    • 0000211724 scopus 로고
    • Multilateral summation theorems for ordinary and basic hypergeometric series in U(n)
    • R.A. Gustafson Multilateral summation theorems for ordinary and basic hypergeometric series in U ( n ) SIAM J. Math. Anal. 18 1987 1576-1596
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1576-1596
    • Gustafson, R.A.1
  • 12
    • 0000474360 scopus 로고
    • Hypergeometric functions with integral parameter differences
    • P.W. Karlsson Hypergeometric functions with integral parameter differences J. Math. Phys. 12 1971 270-271
    • (1971) J. Math. Phys. , vol.12 , pp. 270-271
    • Karlsson, P.W.1
  • 13
    • 0042478949 scopus 로고
    • Operator methods and Lagrange inversion, a unified approach to Lagrange formulas
    • C. Krattenthaler Operator methods and Lagrange inversion a unified approach to Lagrange formulas, Trans. Amer. Math. Soc. 305 1988 431-465
    • (1988) Trans. Amer. Math. Soc. , vol.305 , pp. 431-465
    • Krattenthaler, C.1
  • 15
    • 0008556567 scopus 로고    scopus 로고
    • A new multidimensional matrix inverse with applications to multiple q-series
    • C. Krattenthaler M. Schlosser A new multidimensional matrix inverse with applications to multiple q-series Discrete Math. 204 1999 249-279
    • (1999) Discrete Math. , vol.204 , pp. 249-279
    • Krattenthaler, C.1    Schlosser, M.2
  • 17
    • 21344494894 scopus 로고
    • The Cl Bailey transform and Bailey lemma
    • G.M. Lilly S.C. Milne The C l Bailey transform and Bailey lemma Constr. Approx. 9 1993 473-500
    • (1993) Constr. Approx. , vol.9 , pp. 473-500
    • Lilly, G.M.1    Milne, S.C.2
  • 18
    • 0031572791 scopus 로고    scopus 로고
    • Balanced 3φ2 summation theorems for U(n) basic hypergeometric series
    • S.C. Milne Balanced 3 φ 2 summation theorems for U(n) basic hypergeometric series Adv. Math. 131 1997 93-187
    • (1997) Adv. Math. , vol.131 , pp. 93-187
    • Milne, S.C.1
  • 19
    • 0001132088 scopus 로고
    • Consequences of the Al and Cl Bailey transform and Bailey lemma
    • S.C. Milne G.M. Lilly Consequences of the A l and C l Bailey transform and Bailey lemma Discrete Math. 139 1995 319-346
    • (1995) Discrete Math. , vol.139 , pp. 319-346
    • Milne, S.C.1    Lilly, G.M.2
  • 20
    • 0000016826 scopus 로고
    • Generalized hypergeometric function of unit argument
    • B. Minton Generalized hypergeometric function of unit argument J. Math. Phys. 11 1970 1375-1376
    • (1970) J. Math. Phys. , vol.11 , pp. 1375-1376
    • Minton, B.1
  • 22
    • 0346499268 scopus 로고    scopus 로고
    • Elliptic hypergeometric series on root systems
    • H. Rosengren Elliptic hypergeometric series on root systems Adv. Math. 181 2004 417-447
    • (2004) Adv. Math. , vol.181 , pp. 417-447
    • Rosengren, H.1
  • 23
    • 4644229153 scopus 로고    scopus 로고
    • Reduction formulas for Karlsson-Minton-type hypergeometric functions
    • H. Rosengren, Reduction formulas for Karlsson-Minton-type hypergeometric functions, Constr. Approx. 20 (2004) 525-548.
    • (2004) Constr. Approx. , vol.20 , pp. 525-548
    • Rosengren, H.1
  • 24
    • 21744440083 scopus 로고    scopus 로고
    • r basic hypergeometric series
    • r basic hypergeometric series Ramanujan J. 1 1997 243-274
    • (1997) Ramanujan J. , vol.1 , pp. 243-274
    • Schlosser, M.1
  • 26
    • 0011381022 scopus 로고    scopus 로고
    • r
    • M. Schlosser A new multidimensional matrix inversion in A r Contemp. Math. 254 2000 413-432
    • (2000) Contemp. Math. , vol.254 , pp. 413-432
    • Schlosser, M.1
  • 27
    • 0038282168 scopus 로고    scopus 로고
    • Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q
    • B.C. Berndt, K. Ono (Eds.) Amer. Math. Soc., Providence, RI
    • M. Schlosser, Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q, in: B.C. Berndt, K. Ono (Eds.), q-Series with Applications to Combinatorics, Number Theory and Physics, Contemporary Mathematics 291, Amer. Math. Soc., Providence, RI, 2001, pp. 203-227.
    • (2001) Q-Series With Applications to Combinatorics, Number Theory and Physics, Contemporary Mathematics , vol.291 , pp. 203-227
    • Schlosser, M.1
  • 28
    • 0142192498 scopus 로고    scopus 로고
    • Elementary derivations of identities for bilateral basic hypergeometric series
    • (N. S.)
    • M. Schlosser Elementary derivations of identities for bilateral basic hypergeometric series Selecta Math. (N. S.) 9 2003 119-159
    • (2003) Selecta Math. , vol.9 , pp. 119-159
    • Schlosser, M.1
  • 29
    • 84963090951 scopus 로고
    • Transformations of basic hypergeometric functions of any order
    • D.B. Sears Transformations of basic hypergeometric functions of any order Proc. London Math. Soc. (2) 53 1951 181-191
    • (1951) Proc. London Math. Soc. (2) , vol.53 , pp. 181-191
    • Sears, D.B.1
  • 30
  • 31
    • 0004320895 scopus 로고
    • Éléments de la théorie des fonctions elliptiques
    • Paris: Gauthier-Villars
    • J. Tannery J. Molk Éléments de la théorie des fonctions elliptiques, Tome III: Calcul Intégral 1898 Gauthier-Villars Paris
    • (1898) Tome III: Calcul Intégral
    • Tannery, J.1    Molk, J.2
  • 32
    • 0035982986 scopus 로고    scopus 로고
    • Summation and transformation formulas for elliptic hypergeometric series
    • S.O. Warnaar Summation and transformation formulas for elliptic hypergeometric series Constr. Approx. 18 2002 479-502
    • (2002) Constr. Approx. , vol.18 , pp. 479-502
    • Warnaar, S.O.1
  • 33
    • 0038282168 scopus 로고    scopus 로고
    • Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q
    • B.C. Berndt, K. Ono (Eds.), Amer. Math. Soc., Providence, RI
    • M. Schlosser, Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q, in: B.C. Berndt, K. Ono (Eds.), q-Series with Applications to Combinatorics, Number Theory and Physics, Contemporary Mathematics 291, Amer. Math. Soc., Providence, RI, 2001, pp. 203-227.
    • (2001) Q-Series With Applications to Combinatorics, Number Theory and Physics, Contemporary Mathematics , vol.291 , pp. 203-227
    • Schlosser, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.